IONOSPHERIC RADIO PROPAGATION in .NET

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IONOSPHERIC RADIO PROPAGATION
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TABLE 7.2. [41]: Phase spectra S k per unit mean square uctuation of phase together with the corresponding autocorrelation function r x (inner scale l0 is zero relative to outer scale L0 ) p 2 3 4 5 S k 4L0 1 k2 L2 0 r x   x exp L0   x x K1 L0 L0     x x exp 1 L0 L0    ! x x 1 x x K1 K0 L0 L0 2 L0 L0
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1 k2 L2 3=2 0 8L0 1 k2 L2 2 0 3pL0 1 k2 L2 5=2 0
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Lens action occurs in the screen, producing focal action in the reception plane. As follows from (7.88), the lens scale lL can be de ned through the Fresnel scale lL dF 2 F 2 1=4 7:92
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TABLE 7.3(a). [41]: Autocorrelation function for an outer scale L0 and an inner scale l0 P0 r X x2 l2 1=2 0 exp L0   l0 exp L0 !
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! x2 l2 1=2 x2 l2 1=2 0 0 K1 L0 L0   l0 l0 K1 L0 L0 ! ! x2 l2 1=2 x2 l2 1=2 0 0 exp 1 L0 L0     l0 l0 exp 1 L0 L0 " ! !# x2 l2 1=2 x2 l2 1=2 1 x2 l2 1=2 x2 l2 1=2 0 0 0 0 K1 K0 L0 L0 L0 L0 2    ! l0 l0 1 l0 l0 K1 K0 L0 L0 L0 2 L0
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EFFECTS OF THE INHOMOGENEOUS IONOSPHERE ON RADIO PROPAGATION
TABLE 7.3(b). [41]: Phase spectra per unit mean square uctuation of phase for an outer scale L0 and an inner scale l0 P0
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l   Kl 0 1 K 2 L2 1=2 0 l0 L0 4l0 exp 1=2 L0 1 k2 L2 0 2pl2 0 
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  l0   1 1 k2 L2 1=2 0 l0 L0 2 2 1=2   3 exp 1 k L0 l0 L0 l0 L0 Kl 1 k2 L2 1=2 0 L0 L0 8l4 0 Kl  l0 1 k2 L2 1=2 0 L0 
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   l0 l0 exp L3 1 0 L0 L0 3pd4    0   l0 l0 l0 K0 L3 Kl 0 L0 L0 L0
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  2 l0 1 l0   l k2 L2 1=2 1 K 2 L2 1=2 0 0 l0 L0 3 L0 exp 1 k2 L2 1=2  5 0 L0 l0 1 k2 L2 1=2 0 L0
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    1 l0 l0 1 k2 L2 1=2 K 0 1 k2 L2 1=2 0 0 L0 2 L0  3 l0 2 2 1=2 1 k L0 L0
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Hence, the irregularities with a scale of lL de ned by (7.91b) (7.92) give a focusing effect of a radio wave passing the ionosphere at the Earth s surface. Therefore in Reference [41] this scale was de ned as a lens scale. The focal scale, lF , is de ned as the width of the average focal spots at the reception plane by the scattering of radio waves from the medium- and large-scale ionospheric irregularities. It determines uctuations of radio signal amplitude at the Earth s surface after such a scattering. The focal scale, which varies with the spectral index, is associated with the arrival at the reception plane of an angular spectrum of waves that are approximately co phased within an angle of about l= 2plF of the norm. It is determined as [31,34,41] lF lL 2 F 2 1=2 7:93
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It is seen from (7.93) that for a given scale in the screen, the larger the mean square uctuation of phase, the closer is the focal plane to the screen and the sharper are the foci. The peak scale, lP , represents the peak in the intensity spectrum I k , such that the angular spatial frequency K l 1 gives the low frequency edge of the peak in P the intensity spectrum in the reception plane. When refractive scattering dominates, the reciprocals of the scales lP and lF give the lower and upper roll-off angular spatial frequencies K for the intensity spectrum in the reception plane,
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IONOSPHERIC RADIO PROPAGATION
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TABLE 7.4. [31,41]: The focal scale lF and the peak scale lP for large L0 =dF and 2 Spectral Index p0 3.5
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